Question

A line segment beginning at point A(−7,−10) and ending at point B(5,8) is drawn on a coordinate plane. Point C(−3,−4) is plotted on AB⎯⎯⎯⎯⎯⎯⎯ . Point C divides AB⎯⎯⎯⎯⎯⎯⎯ into a ratio of : . (Express the ratio in simplest integer form.)

Answer 1

The total x-distance from A to B is 5 - (-7) = 12.

The x-distance from C to A is -3 -(-7) = 4.

Then the x-distance from C to B is 12 - 4 = 8.

The ratio AC : CB is 4 : 8. These ratio values have a common factor of 4, so we can divide by that to get the simplest integer form:

... AC : CB = 1 : 2 . . . . . the ratio into which point C divides the line segment.

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If you perform the same math on y-coordinates, you should get the same answer. If you don't, it means that point C is not on the line AB.